This is possible as of iOS 7.
To disable certain apps' ability to use Cellular Network data, open the Settings.app and select "Cellular". Scroll down and you will notice a list of Apps which request cellular data access. These are all on by default.
This list is helpful for two things: first, you can see which apps have consumed the most data; second, you can disable certain apps from using the cellular data network. Keep in mind, when you disable that app, it is only preventing it from using the cellular network, and the app will still function normally on wifi. You can now go through and curate the list as you see fit. Even system apps, such as Mail, and Settings, are in the list.
At the bottom of the list, you can see another line titled System Services. In there is a list of non-adjustable services that use the data connection. It will tell you how much data has gone to each one. You can use this list to determine if you should make any other changes. For example, Personal Hotspot is at the top of my list. This doesn't surprise me and is fine. However, for you, if it is at the top of your list and you doesn't use that feature, this could be a concern, and you should verify that the feature is disabled. Also, Siri (if your device supports it), and iMessages are in the list. Both of the features can be disabled elsewhere in the Settings.app.